We compare three algorithm choices: HICU, HICU paired with SWT (HICU+SWT), and HICU paired with DNN denoiser (HICU+DNN). A comparison of HICU to other calibrationless reconstruction methods is reported in [1]}. We use 119 T2 weighted brain datasets \(D1\)  to \(D119\)  from fastMRI [2]} to benchmark the reconstruction. All datasets were fully sampled and collected in an axial orientation on 3 T scanners using a T2-weighted turbo spin-echo sequence. Other imaging parameters included: TE 113 ms, TR 6,000—6,570 ms, TI 100 ms, field-of-view (FOV) 220 mm\( \times \)  227 mm, slice thickness 7.5 mm, matrix size 384\(\times \) 384, number of receive coils 16—20, and flip angle 149—180 degrees. The center slice from each dataset was used. The sampling patterns and acceleration rates are shown in Figure REF . For all three algorithm choices, rank \(r = 30\) , which is chosen based on one additional dataset for sampling pattern \(S2, R=5\) . The filter kernel size is \(3 \times 3 \times N_c\) , where \(N_c\)  is the number of coils; valid convolution is computed without the need for data padding. CO processing is organized simply as two stages. The first uses the center \(1/4 N_x \times 1/4 N_y \times N_c\)  portion of k-space, \(p = 8\) , and iteration count \(G_i = 5\)  (Step 6). The second stage uses the full k-space, \(p = 32\) , and iteration count \(G_i = 10\) . The number of outer iterations (\(I\)  in Step 1) dedicated to the first CO stage was tuned based on the same additional dataset to achieve fast convergence and was held constant for all six combinations of sampling patterns and acceleration rates. Computation in all cases was terminated at one minute. For computational speed, both HICU+SWT and HICU+DNN only apply the denoiser (Step 10) in the second CO stage.
